Which hands should the small blind shove at 4bb?
The small blind posts half a big blind and acts first. With 4 big blinds behind, the solved chart shoves 73.8% of hands, which is 978 of the 1,326 two-card holdings, and folds the rest for the half blind already posted.
In shorthand the shoving range is 22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 93s+, 84s+, 74s+, 64s+, 54s, A2o+, K2o+, Q2o+, J2o+, T5o+, 96o+, 86o+, 76o. By equity against a random hand, 64s is the lowest-ranked hand that still shoves and T4o is the highest-ranked hand that folds. No hand mixes here: every hand either shoves or folds, so the chart has no coin flips.
Small blind shove chart at 4 big blinds heads-up. Shoves: 22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 93s+, 84s+, 74s+, 64s+, 54s, A2o+, K2o+, Q2o+, J2o+, T5o+, 96o+, 86o+, 76o.
- Shove
- Mixes
- Fold
- Under 50% equity
Which hands should the big blind call with at 4bb?
At 4bb the big blind calls a shove with 74.1% of hands, which is 982 of the 1,326 combos, and folds all others.
In shorthand the calling range is 22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 93s+, 84s+, 74s+, 64s+, 53s+, A2o+, K2o+, Q2o+, J2o+, T5o+, 96o+, 86o+, 76o. By equity against a random hand, 53s is the lowest-ranked hand that still calls and T4o is the highest-ranked hand that folds. No hand mixes here: every hand either calls or folds, so the chart has no coin flips.
Big blind call chart at 4 big blinds heads-up. Calls: 22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 93s+, 84s+, 74s+, 64s+, 53s+, A2o+, K2o+, Q2o+, J2o+, T5o+, 96o+, 86o+, 76o.
- Call
- Mixes
- Fold
- Under 50% equity
Which kinds of hands make up the 4bb ranges?
Pairs, suited hands and offsuit hands thin out at different speeds as the stack grows. The table counts the hands of each kind that act at 4bb, out of the 13 pairs and the 78 suited and 78 offsuit hands, and the share of each kind's specific combos that act once mixed hands are weighted by how often they act.
| Kind | Small blind shoves | Share of combos | Big blind calls | Share of combos |
|---|---|---|---|---|
| Pairs | 13 of 13 | 100.0% | 13 of 13 | 100.0% |
| Suited hands | 66 of 78 | 84.6% | 67 of 78 | 85.9% |
| Offsuit hands | 53 of 78 | 67.9% | 53 of 78 | 67.9% |
Which decisions are closest at 4bb?
A hand's edge is its EV for acting minus the EV of folding, in big blinds. Folding is worth -0.500 for the small blind and -1.000 for the big blind facing a shove. Hands with an edge near zero change their answer first as the stack moves.
| Hand | Rank of 169 | Shove EV | Fold EV | Edge | Equity when called | Chart |
|---|---|---|---|---|---|---|
| T5o | 122 | -0.483 | -0.500 | +0.017 | 37.6% | Shove |
| 93s | 126 | -0.479 | -0.500 | +0.021 | 38.0% | Shove |
| 76o | 133 | -0.471 | -0.500 | +0.029 | 37.7% | Shove |
| 53s | 146 | -0.508 | -0.500 | -0.008 | 37.7% | Fold |
| 92s | 132 | -0.518 | -0.500 | -0.018 | 37.3% | Fold |
| T4o | 125 | -0.521 | -0.500 | -0.021 | 37.1% | Fold |
| Hand | Rank of 169 | Call EV | Fold EV | Edge | Equity vs shoves | Chart |
|---|---|---|---|---|---|---|
| T5o | 122 | -1.000 | -1.000 | +0.000 | 37.5% | Call |
| 76o | 133 | -0.991 | -1.000 | +0.009 | 37.6% | Call |
| 53s | 146 | -0.985 | -1.000 | +0.015 | 37.7% | Call |
| 92s | 132 | -1.019 | -1.000 | -0.019 | 37.3% | Fold |
| 43s | 150 | -1.034 | -1.000 | -0.034 | 37.1% | Fold |
| T4o | 125 | -1.043 | -1.000 | -0.043 | 37.0% | Fold |
Which seat is ahead at 4bb?
At 4bb the small blind's seat is worth +0.066 big blinds per hand dealt, so the shove range steals enough blinds to come out ahead of the big blind's seat. The small blind stays ahead until the stack reaches 8bb, where the value per hand turns negative. Value per hand dealt counts folds, shoves and calls together, from the start of the hand before the blinds go in.
How does the chart change around 4bb?
| Stack | Small blind shoves | Big blind calls | Small blind value per hand |
|---|---|---|---|
| 2bb | 89.4% | 100.0% | +0.010 |
| 3bb | 78.0% | 92.3% | +0.052 |
| 4bb | 73.8% | 74.1% | +0.066 |
| 5bb | 71.5% | 62.1% | +0.056 |
| 6bb | 68.3% | 54.4% | +0.038 |
Going from 3bb to 4bb, T4o, 95o, T3o, 92s and 85o leave the small blind's shoving range; T4o, 95o, T3o, 92s, T2o and 22 more leave the big blind's calling range.
The biggest single move for the small blind between 3bb and 4bb is 92s, which goes from shoving 100% of the time to 0%. For the big blind it is 92s, from calling 100% of the time to 0%.
Only the smaller stack can be won or lost, so the chart is read at the effective stack. A player with 4 big blinds behind uses the 4bb chart whatever the other stack is, if it is bigger.
Where can I check one hand or a different stack?
Pick a hand below to see where it flips, or open the calculator for any hand at any stack from 1 to 20 big blinds. The ICM pages show what changes with prize money.
How was this chart computed?
We solve a chips-only game for two players: small blind 0.5, big blind 1, no ante, equal stacks. Starting hands are the 169 classes, weighted so that shared cards are impossible, and equity comes from counting every five-card board. The solver plays itself with best responses, averages them, and fixes the hands on the edge so they are exactly indifferent. Exploitability is the most the two players could gain together by switching to a best response, in big blinds per hand. At 4bb the published strategies have an exploitability of under 0.000001 big blinds per hand, against a limit of 0.001.
Source: GeorgeLiPoker's own heads-up solver, run on its exact preflop equity table.
Questions
- What is the push or fold range at 4bb heads-up?
- The small blind shoves 22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 93s+, 84s+, 74s+, 64s+, 54s, A2o+, K2o+, Q2o+, J2o+, T5o+, 96o+, 86o+, 76o, which is 73.8% of hands. The big blind calls 22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 93s+, 84s+, 74s+, 64s+, 53s+, A2o+, K2o+, Q2o+, J2o+, T5o+, 96o+, 86o+, 76o, which is 74.1% of hands. Both ranges are for a chips-only game with blinds of 0.5 and 1 and no ante.
- Is T5o a shove at 4bb?
- T5o is one of the closest decisions on the small blind chart. Shoving is worth -0.483 big blinds against -0.500 for folding, so the chart shoves it, and it is rank 122 of 169 by equity against a random hand.
- Should the big blind call with 92s at 4bb?
- The chart folds it, narrowly. Calling is worth -1.019 big blinds against -1.000 for folding, and its equity against the shoving range is 37.3%.